Theorems · Theorem · general topology

EMetric.tendsto_nhds

∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] {f : Filter β} {u : β → α} {a : α},
  Filter.Tendsto u f (nhds a) ↔ ∀ ε > 0, ∀ᶠ (x : β) in f, edist (u x) a < ε

Defined in

Mathlib.Topology.EMetricSpace.Defs

Cited by

4 results in Mathlib

Foundations

Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpace